
where \(p_0(\mathbf {x})\)  is typically a uniform distribution over \([-1,1]\) . Note that this is similar to SGLD (see Eq. REF ) but without a noisy term. Thus, the training could be more stable. In addition, the function \(E_{\mathbf {\theta }}(\mathbf {x}^{\prime })=\frac{1}{2\gamma ^2}||\mathbf {\phi }(\mathbf {x}^{\prime })-\mathbf {z}_{\mathbf {x}^{\prime }}||_2^2\)  is just an \(L_2\)  regression loss (not an LogSumExp function as used in JEM [1]}). This may lead to additional numerical stability.
